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September Diary
On the Sovereignty Caucus, Chris Christie, the existence of evil, and more.


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John Derbyshire


Smoking through an operation. The Age of Tobacco is now receding into history. It’s already hard to recall how universal cigarette smoking once was.

People even smoked in hospitals — heck, I can remember that. I didn’t realize how far it went, though, until I read this in the Fefermans’ biography of logician Alfred Tarski. The subject here is Stanisław Leśniewski, who had been Tarski’s dissertation adviser at the University of Warsaw. Leśniewski is having surgery for thyroid cancer. This is 1939.

The operation was conducted without anaesthetic, because the anaesthesiology of the time had no methods which did not constrict the blood vessels around the thyroid. He was permitted to smoke during the operation!

The Fefermans caution that this account — it’s by one of Leśniewski’s students, not Tarski — “may be inaccurate since it contradicts known surgical procedure.” From what I recall of the Age of Tobacco, though, I wouldn’t be surprised if it were true.

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Math Corner. This month’s puzzle is from a reader, an engineer, who tells me: “This puzzle arose out of work I was doing for a client, Solyndra.”

Hmm, rings a bell. Anyway, here’s the puzzle:

It is a tiling problem of sorts, arising out of placing solar panels on a roof.

We wish to mount a group of solar panels on a roof. Let’s use 15 as an example. The mounting system requires that each panel touch at least one other along an edge. The panels are rectangular, and all must be oriented the same way.

Obviously we could create a 3×5 grid. We could simply string the 15 panels in a row. We could create a 4×4 grid with one hole. There are many, many combinations that meet the constraints. But, for a given number of panels, exactly how many?

(On a practical basis, this comes up because roofs have projections — chimneys, vents, etc. — and you must install around them. We usually solve it empirically.)

After a fair amount of noodling, I decided I didn’t have enough math to solve it. It’s easy, for example, to determine the number of ways you can select 15 items from a set of 225 (15×15) but many of those selections are illegal. Panels must be coterminous along at least one edge.

Is this trivially simple? Or interesting? Or brute-force only?



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